You hope to rent an unfurnished one-bedroom apartment in Dallas next year. You call a friend who lives there and ask him to give you an estimate of the mean monthly rate. Having recently taken a statistics course, your geeky friend asks about the desired margin of error and confidence level for the estimate. He also tells you that the standard deviation of monthly rents for one-bedrooms is $ 360. Layth C. Alwan; Bruce A. Craig; George P. McCabe. The Practice of Statistics for Business and Economics (Kindle Locations 23101-23103). W. H. Freeman. Kindle Edition.
(a) For 95% confidence and a margin of error of $150, how many apartments should the friend randomly sample from the local newspaper?
(b) Suppose that you want the margin of error to be no more than $50. How many apartments should the friend sample?
(c) Why is the sample size in part (b) not just nine times larger than the sample size in part (a)?